FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables
In a multiple regression, a researcher finds that two explanatory variables have a sample correlation of 0.98, the overall F-test is highly significant, yet neither variable's individual t-statistic is significant. Which OLS assumption problem is most consistent with this pattern?
The pattern indicates imperfect multicollinearity. A 0.98 correlation between regressors inflates the standard errors of the individual slopes, so t-tests are insignificant even though the regressors jointly explain Y and the F-test is significant. Estimation remains possible because the correlation is not perfect.
- APerfect multicollinearity, which makes OLS estimates impossible to compute
- BImperfect multicollinearity, which inflates standard errors of the slope estimatesCorrect
- CHeteroskedasticity, which biases the slope estimates
- DOmitted variable bias from a variable uncorrelated with both regressors
Explanation
High but not perfect correlation among regressors inflates coefficient standard errors, producing insignificant t-statistics while joint significance remains. Perfect multicollinearity would prevent estimation altogether, and the correlation here is 0.98, not 1. Heteroskedasticity affects standard errors but does not bias slopes and does not explain this pattern.
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